The 2004 Indonesian and 2010 Chilean Earthquakes and Earth's Rotation

Since the great 2004 Indonesian earthquake I have gotten numerous inquiries
about whether the earthquake affected the earth's axis.

What was affected was the so-called Chandler Wobble. Objects that are not
perfectly spherical do not rotate around a single axis. That's just the laws
of physics. I did the math in graduate school. Unless you know tensors, you
don't want to go there. Anyway, the earth doesn't rotate smoothly around its
axis, instead, the poles wander in rough circles about 10 meters in diameter.
Another way to say it is your latitude changes a bit (0.7 seconds of arc) over a
cycle of about a year. Anything that redistributes mass on the earth, even
weather systems and the circulation of the oceans, can affect this wobble
detectably. Think of a bunch of people on a merry-go-round all running over to
one side. Since we can routinely locate ourselves nowadays to accuracies of
meters, and precise surveys can locate points to millimeters, we can detect even
these tiny changes. What happened here was a big chunk of the northern Indian
Ocean lurched northward 10-20 meters relative to Asia. It also descended several
meters into the mantle, and compressed and elevated northern Sumatra by several
meters. It also likely triggered big submarine landslides that caused the
tsunamis. So a fair amount of mass got redistributed. The U.S. Naval Observatory
tracks this stuff and will tell you all you want to know about it, but I haven't
see anything posted about the big quake yet. However, the US Geological Survey
posted this:

Question: What effect did this earthquake have on the rotation of the
earth? Answer: Richard Gross at JPL has modeled the coseismic effect on the
Earth's rotation of the December 26 earthquake in Indonesia by using the
PREM model for the elastic properties of the Earth and the Harvard centroid-moment
tensor solution for the source properties of the earthquake. The result is:

change in length of day: -2.676 microseconds

polar motion excitation X : -0.670 milliarcseconds

polar motion excitation Y: 0.475 milliarcseconds

Since the length of the day can be measured with an accuracy of about 20
microseconds, this model predicts that the change in the length-of-day
caused by the earthquake is much too small to be observed. And, since the
location of the earthquake was near the equator, this model predicts that
the change in polar motion excitation is also rather small, being about 0.82
milliarcsecond in amplitude. Such a small change in polar motion excitation
will also be difficult to detect.

Note this is a calculation, not an observation. What it means is the day
became shorter by 0.0000027 seconds (Great - I don't have enough time as it
is!). It will take about 1,000 years for that to throw the earth out of sync
with clocks by one second, and other things like tidal friction will have much
greater effects. The excitation is the motion of the actual pole, around which
the earth is rotating at any given instant, compared to the "average" pole we
use on maps and globes. One second of arc is 30 meters, or 3000 centimeters, so
0.8 milliseconds is 2.5 centimeters or about an inch.

How exactly did the earthquake change the earth's rotation speed? It seems to
have done so because the earthquake involved plate convergence, and effectively
reduced the earth's equatorial circumference by a few millimeters while pushing
denser material into the earth, like an ice skater pulling in her arms. That would
also reduce the earth's equatorial radius a fraction of a millimeter. The overall
fault slip was 10-20 meters, but some of that was directed north-south, so the
east-west compression was smaller. The effect would be further reduced by
the fact that the crust above the fault zone would have been uplifted, resulting
in a bulge that would somewhat offset the reduction in circumference. Not all
the local compression would affect the equator anyway, just like buttoning a
shirt that's too tight pulls your waist in a little, but not as much as the gap
between the last buttons.

The Earth's rotational properties are described by its moment of inertia,
which is proportional to the square of its equatorial radius. The calculated
change in rotation rate is about 3 x 10-11 of the length of the day,
implying a similar change of 3 x 10-11 in the earth's equatorial radius
(about 0.4 millimeters) or about 2.4 millimeters (1/10 inch) shortening of the equatorial
circumference.

The Chilean earthquake of 2010 likewise produced calculated changes of a few
microseconds in the length of the day and a few centimeters in the positions of
the poles, and for the same reasons. A sudden shift of mass into the earth
speeds up the rotation a tad, just like an ice skater drawing in her arms.

Long term, however, the earth is not going to suck into a black hole like the
planet Vulcan in the Star Trek reboot. Matter is also rising out of the
earth in the form of hot light mantle material at mid ocean ridges, as well as
uplift of mountains. So overall we'd expect those motions to slow down the
earth's rotation, but more gradually than the speedups due to earthquakes.
Overall, the two effects should balance on a long time scale. If we could
actually measure the effects, we'd likely see a saw-tooth graph with abrupt
increases in rotation speed during big earthquakes and gradual increases in
between, more or less erasing the speedups.